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Popular >

derivative of y=cos(x)sin(x)

Solution

derivative of

y = cos (x) sin (x)

Solution

cos (2 x)

Solution steps

\frac{d}{d x} (cos (x) sin (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos (x), g = sin (x)

= \frac{d}{d x} (cos (x)) sin (x) + \frac{d}{d x} (sin (x)) cos (x)

\frac{d}{d x} (cos (x)) = - sin (x)

\frac{d}{d x} (sin (x)) = cos (x)

= (- sin (x)) sin (x) + cos (x) cos (x)

Simplify

(- sin (x)) sin (x) + cos (x) cos (x) : cos (2 x)

= cos (2 x)

Popular Examples

integral of 2/(x^2-3x+2)

\int \frac{2}{x ^{2} - 3 x + 2} d x

(\partial)/(\partial x)(cos(x+8y))

\frac{\partial}{\partial x} (cos (x + 8 y))

integral from 0 to ln(2) of (e^{3x})/(1+e^{6x)}

\int_{0}^{l n (2)} \frac{e ^{3 x}}{1 + e ^{6 x}} d x

x*(dy)/(dx)+2y=3

x \cdot \frac{d y}{d x} + 2 y = 3

derivative of 5-|x-5|

\frac{d}{d x} (5 - ∣ x - 5 ∣)

Frequently Asked Questions (FAQ)

What is the derivative of y=cos(x)sin(x) ?
The derivative of y=cos(x)sin(x) is cos(2x)
What is the first derivative of y=cos(x)sin(x) ?
The first derivative of y=cos(x)sin(x) is cos(2x)